I’ve experienced similar. Once things go awry with a scheduled flight the situation can degrade quickly. In my experience, having done 100’s of flights, they start to lie. The lies start to contradict each other - this is when tempers start to flare. I usually give them a single delay, if they delay again, I reschedule if possible. I’m not wasting my time with a situation which you describe, been there too. They put you in an exhausting situation with no reasonable recourse.
It seems everything revolves around processes which assume things go right, herding you on & off flights. If anything goes wrong all of the negative consequences fall on the customer.
I had an experience similar where a storm rolled in at a layover location, where lies about delays (resulting in complete cancellation) left people unable to go to a hotel. What made me angry was seeing the elderly trying to sleep ON THE FLOOR, as they don’t have cots or a space for anyone, while all the lights, TV volume, AND CLEANING CREW schedule all remained unchanged. Seeing cleaning staff vacuum the floor and going right up to their heads p*ssed me off. The excuse for the airline was that they don’t control the terminal but were unwilling to even try to contact somebody that could make the situation just a little bit better (e.g. turn off some lights? turn down TV volume?) - as no flights were going in or out and it was 3am.
The other excuse was “this is rare”....but is it? It may not happen at a given airport very often but is probably happening every day somewhere. The airlines should be required to have some better accommodations when this happens. People weren’t being treated with any care or dignity.
Airlines once put you up in the airport Hilton and sent you thee with a bag of essentials. Now they ignore you.